Phonon dispersions: Performance of the generalized gradient approximation

By computing the phonon dispersions of a few selected solids (Si, C, Al, an d Cu), within density-functional perturbation theory, we compare the perfor mance of the local density approximation (LDA) with that of the generalized gradient approximations (GGA's) in the form recently proposed by Perdew, B urke, and Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)]. We find that GGA sy stematically lowers the frequencies of phonon branches with positive Grunei sen parameters. This effect is correlated with the GGA's expansion of the l attice constant, since GGA phonon frequencies computed at the experimental lattice constants are higher than the corresponding LDA ones. In C, Al, and Cu, LDA and GGA phonon dispersions have similar accuracy with respect to t he experimental data. Si is an exception since the LDA phonon dispersions a re already in very good agreement with experiment and GGA worsens the compa rison. [S0163-1829(99)03339-1].